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Search: id:A002699
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| A002699 |
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n*2^(2*n-1).
(Formerly M2090 N0825)
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+0
3
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| 0, 2, 16, 96, 512, 2560, 12288, 57344, 262144, 1179648, 5242880, 23068672, 100663296, 436207616, 1879048192, 8053063680, 34359738368, 146028888064, 618475290624, 2611340115968, 10995116277760, 46179488366592, 193514046488576
(list; graph; listen)
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OFFSET
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0,2
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COMMENT
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Right side of binomial sum Sum(i * binomial(2*n, i), i=1..n) - Yong Kong (ykong(AT)curagen.com), Dec 26 2000
Coefficients of shifted Chebyshev polynomials.
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REFERENCES
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
C. Lanczos, Applied Analysis. Prentice-Hall, Englewood Cliffs, NJ, 1956, p. 518.
A. P. Prudnikov, Yu. A. Brychkov, and O.I. Marichev, "Integrals and Series", Volume 1: "Elementary Functions", Chapter 4: "Finite Sums", New York, Gordon and Breach Science Publishers, 1986-1992.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Index entries for sequences related to Chebyshev polynomials.
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MAPLE
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A002699 := n->n*2^(2*n-1);
A002699:=2*z/(4*z-1)**2; [Conjectured by S. Plouffe in his 1992 dissertation.]
with(finance):seq(add(futurevalue( 2, 3, n), k=0..n), n=-1..21); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jun 20 2008
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CROSSREFS
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Found in A053125 and A053124.
Cf. A002697.
Adjacent sequences: A002696 A002697 A002698 this_sequence A002700 A002701 A002702
Sequence in context: A000431 A141243 A038749 this_sequence A005058 A082639 A043016
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KEYWORD
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nonn,easy,nice
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AUTHOR
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njas
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